Mazzarri's position has come under scrutiny with Inter sitting ninth in the Serie A table following three defeats from their first 10 games.
The ambitious Thohir is expecting the San Siro outfit to surge up the league and silence their critics, with the derby against Milan and a clash with Roma to come after Sunday's encounter with Verona.
"Do I have a message for the fans to stop jeering the team and coach at San Siro? No, no, I am not the one who has to send a message to anyone," he told La Gazzetta dello Sport.
"It is the team on the field who must send a good message to the fans and I hope they will.
"Now we will think of Verona. We must concentrate only on that game and have to get points. I am convinced the team will do well on Sunday, but the fact remains I expect to get points over the next three games.
"I know the difference between one and three points means a victory, but I'd really like the next matches to bring points – plural.
"I say that because the real challenges will be against Milan and Roma, which can give us an important push up the table."
Sampdoria coach Sinisa Mihajlovic has been linked with Inter following the Genoa club's encouraging start to the campaign.
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